Question

Find the cube root of $13824$ by the prime factorization method.

Answer 1

Evaluate the Cube Root:

The given number is $13824$.

After resolving the prime factors, we get

$13824=2x2x2x2x2x2x2x2x2x3x3x3$

Upon grouping the factors we get

$13824=(2x2x2)x(2x2x2)x(2x2x2)x(3x3x3)$

Taking one factor from each group

$\sqrt[3]{13824}=2x2x2x3$

$=24$

Hence, the required cube root is $24$.